Question

For the function $f\left(x\right)=x^2-2x-8$

(a) find $x$when$f\left(x\right)=7$

(b) Find two points that lie on the graph of the function.

Short answer

The value of $x$is $-3,5$and the points lying on the graph is$(0,-8),(1,-9)$

Step-by-step solution

Given information 

Given the equation$f\left(x\right)=x^2-2x-8$

Substitute f(x)=7 and calculate the value

Substituting the value, we get

$$\begin{gathered} 7=x^2-2x-8 \\ {x}^2-2x-15=0 \\ {x}^2-5x+3x-15=0 \\ x(x-5)+3(x-5)=0 \\ (x+3)(x-5)=0 \\ x=-3,5 \end{gathered}$$

Calculate the corresponding y values 

The values are $(0,-8),(1,-9)$the graph of which is